Spatio-temporal variation characteristics of extreme precipitation over the Dongting Lake basin

The Dongting Lake is the second largest freshwater lake in China. The whole basin has a well-developed water system and a relatively concentrated population. The total area of the basin reaches 262,800 km², including the Dongting Lake area and four main tributaries of the Xiangjiang River, the Yuanshui River, the Zishui River and the Lishui River, as well as medium and small rivers such as the Miluo River and the Xinqiang River. Rainfall resources in the Dongting Lake basin are relatively concentrated, and rainstorms occur frequently in the flood season (from April to September). Previous scholars have done some research on the inter-annual and seasonal variation characteristics of precipitation (Song et al. 2012; Zhang & Liu 2016; Guo et al. 2020) and flood risk assessment in the Dongting Lake basin (Gao et al. 2007; Wang et al. 2011). The extreme precipitation in the rainy season is one of the most common meteorological disasters causing flood disasters in the Dongting Lake basin.

Under the background of global climate change, the frequency and intensity of extreme precipitation in the central and eastern China show an increasing trend (Chen et al. 2010; Sun & Zhang 2017). In the study of spatio-temporal variation characteristics of extreme precipitation, Huang et al. (2021) used 12 extreme precipitation indices and the best-fitting extreme value distribution to analyze the spatio-temporal characteristics of extreme precipitation in the upper reaches of the Hongshui River Basin.

Previous studies on the Dongting Lake basin mostly focused on the climate change trend of precipitation. Zhang et al. (2017) used the methods of linear regression and ensemble empirical mode decomposition to analyze the changes of seven extreme precipitation indexes such as the annual precipitation sum during the days with the daily precipitation greater than the 95% quantile and the number of consecutive wet days at 28 meteorological stations in the Dongting Lake basin, and also found that the precipitation in the Dongting Lake basin has a similar increasing trend as the study of Chen et al. (2010) and Sun & Zhang (2017). In terms of spatio-temporal variation characteristics of the extreme precipitation in the Dongting Lake basin, Long et al. (2020) used the self-organizing map-based k-means (SOM-k) method to spatially cluster the extreme precipitation at 85 meteorological stations in the rainy season of the Dongting Lake basin and divided its distributions into three typical types of the southern pattern, the central pattern and the northern pattern, with each pattern appearing mainly in June. Li et al. (2019) studied the spatio-temporal variation characteristics of the extreme precipitation at 14 meteorological stations in the Zishui River basin of the Hunan Province using the empirical orthogonal function (EOF) decomposition and spatial autocorrelation analysis. It was found that extreme precipitation was spatially polarized, and there was a significant increasing trend in the middle and lower reaches of the Zishui River basin. Luo (2019) analyzed the spatio-temporal variation of summer heavy rainfall at 91 meteorological stations in the Dongting Lake basin and corresponding circulation characteristics. It was found that there was an increasing trend for the heavy rainfall in summer, and the increase was more significant in the central region. The variation of summer heavy rainfall was closely related to the western Pacific subtropical high.

The statistical analysis methods used in the above researches can only reveal the climatic variation characteristics from the occurrence frequency, the intensity evolution trend and the spatial distribution pattern of extreme precipitation in the Dongting Lake basin, but cannot fully present the spatio-temporal variation of extreme precipitation. Based on the daily precipitation data at 97 national meteorological stations in the Dongting Lake basin (Figure 1) from 1960 to 2016, this study systematically studies the spatio-temporal variation characteristics of annual maximum daily precipitation and annual maximum accumulated precipitation in a single rainfall event in the whole basin using several analytical methods such as the EOF decomposition, the global Moran's I index, the linear regression method, the Mann–Kendall test and the complex Morlet wavelet transform, in order to comprehensively reveal the climatic characteristics of extreme precipitation in the Dongting Lake basin and provide a useful reference for the flood prevention operation.

In the section ‘Data and methods’, we introduce the analytical methods and the data set used in our analysis. Spatial distribution, EOF decomposition, spatial autocorrelation analysis, variation and abrupt change analysis, and periodic analysis of extreme precipitation are studied in the section ‘Spatio-temporal variation characteristics of extreme precipitation in the Dongting Lake basin’. Finally, section ‘Conclusions and discussion’ summarizes the main conclusions from our study and analyzes some possible follow-up studies.

Based on the daily precipitation data at 97 meteorological stations in the Dongting Lake basin from 1960 to 2016, the day with the precipitation greater than 0.1 mm is regarded as a precipitation day, and the continuous rainfall lasting for 2 days or more is regarded as a single rainfall event. Also, the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event at 97 meteorological stations are, respectively, counted.

The EOF decomposition (Wei 2007; Wilks 2011) and the global Moran's I (Moran 1950; Li et al. 2007) are used in this study to analyze the spatio-temporal variation of extreme precipitation. The linear regression and the Mann–Kendall test (Wei 2007; Wilks 2011) as well as the complex Morlet wavelet transform (Morlet 1983; Lau & Weng 1995) are used to analyze the inter-annual variations and periodic oscillations of precipitation.

The EOF decomposition is also known as the principal component analysis. It is often used to reduce a data set containing a large number of variables to a data set containing fewer new variables. These new variables (principal components) are linear combinations of the original variables, and they are chosen to represent the maximum possible fraction of the variability contained in the original data (Wilks 2011). The linear regression and the Mann–Kendall test are two classical methods for determining whether a time series has a monotonic upward or downward trend. The latter could be more useful and robust, as it does not require that the data be normally distributed or linear. It does require that there is no autocorrelation. The complex Morlet wavelet transform is an analytical method suited to the study of multiscale, non-stationary processes occurring over finite spatio-temporal domains (Lau & Weng 1995). It offers an intuitive bridge between frequency and time information, and can be used as a supplement for the Fourier transform.

The statistic known as Moran's I is widely used in the fields of geography and geographic information science to measure spatial autocorrelation based on both feature locations and feature values simultaneously. Since it is not very familiar to meteorologists, this method is briefly introduced as follows.

The spatial distributions of extreme annual maximum daily precipitation (Figure 2(a)), extreme annual maximum accumulated precipitation in a single rainfall event (Figure 2(b)), averaged annual maximum daily precipitation (Figure 2(c)) and averaged annual maximum accumulated precipitation in a single rainfall event (Figure 2(d)) in the Dongting Lake basin from 1960 to 2016 (57 years in total) are all uneven, and the large-value centers are mainly located in the Lishui River basin and east of the main stream of the Xiangjiang River. The extreme annual maximum daily precipitation in the Zhangjiajie City of the Lishui River basin is 455.5 mm (the averaged annual maximum daily precipitation is 109.9 mm), and that in the Wugang City of the Zishui River basin is 116.5 mm (the averaged annual maximum daily precipitation is 73.5 mm), which is the minimum in the study area. The distribution of accumulated precipitation in a single rainfall event has two large-value centers of the Lishui River basin and the lower reaches of the Xiangjiang River. The maximum value is located in the Liuyang City of the Xiangjiang River basin with the value of 658.4 mm (the averaged annual maximum accumulated precipitation in a single rainfall event is 205.4 mm), and the minimum value is located in the Zhenyuan County of the Yuanshui River basin (belonging to the Miao and Dong Autonomous Prefecture in the southeastern Guizhou Province) with the value of 212.9 mm (the averaged annual maximum accumulated precipitation in a single rainfall event is 126.5 mm).

The averaged annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event in each sub-basin are shown in Table 1. The averaged annual maximum daily precipitation and the accumulated precipitation in a single rainfall event in the Lishui River basin are the largest in the Dongting Lake basin. The averaged annual maximum daily precipitation and the averaged annual maximum accumulated precipitation in a single rainfall event in the Zishui River basin are the smallest in the four sub-basins. Although the averaged annual maximum daily precipitation in the Dongting Lake area is relatively large, the averaged annual maximum accumulated precipitation in a single rainfall event is the smallest there.

In summary, the spatial distribution of extreme precipitation in the Dongting Lake basin presents a characteristic of being large in the Lishui River basin and east of the main stream of the Xiangjiang River, whereas being small in other regions. The area from the northern foot of the Xuefeng Mountain to the southern foot of the Wuling Mountain is the large-value area of extreme precipitation in the whole basin, whereas the small-value area is located in the Xiangzhong Basin, which is mainly caused by the topography differences. Owing to the dynamic lifting and terrain blocking, the windward slope of the mountains and the areas with large topographic relief can often significantly strengthen the duration or intensity of the weather system, which is more conducive to the occurrence of extreme precipitation. However, the terrain lifting in the lake area and the basin is less than that in the mountain area, so the extreme precipitation is also less. To a certain extent, the distribution characteristics of precipitation present the influence of Meiyu-front rainstorms on the northwestern Hunan, Lishui River basin and Dongting Lake area, as well as the influence of typhoon rainstorms east of the mainstream of the Xiangjiang River.

It should be pointed out that the quantitative relationship between the extreme precipitation and the topography is not clear. The distribution of extreme precipitation obtained by the interpolation method of radial basis function can only qualitatively reflect the distribution of extreme precipitation without quantitative significance.

The EOF decomposition of extreme precipitation in the Dongting Lake basin from 1960 to 2016 is carried out in order to reveal the spatial variation characteristics of annual maximum daily precipitation and annual maximum accumulated precipitation in a single rainfall event (Figure 3). The decomposition results of the two elements show that the first and second eigenvectors mainly indicate two modes of ‘north–south pattern’ and ‘northwest–southeast pattern’. For the annual maximum daily precipitation, the variance contribution rates of the first two eigenvectors are 14.1 and 9.1%, respectively. The positive area of the first eigenvector is located to the south of 27°N in the basin, and its center is located in the upper reaches of the Zishui River and the middle and upper reaches of the Xiangjiang River with the value of 0.06. The negative area is located to the north of 27°N, and its center is located in the middle and lower reaches of the Yuanshui River with the value of −0.26. Therefore, the variability of annual maximum daily precipitation in the region north of 27°N is greater. It is more sensitive to climate change there, and it is easier to show floods or droughts (Figure 3(a)). The second eigenvector field is relatively complex, and the positive area presents two long-narrow belts along the direction of southwest–northeast. One is located in the Wuling Mountain area of the northwestern basin, and the other is located in the Xiangzhong Basin of the central basin. The negative area is mainly located in the southeastern Hunan with the central value of −0.38 (Figure 3(b)).

For the annual maximum accumulated precipitation in a single rainfall event, the variance contribution rates of the first two eigenvectors are 21.9 and 12.0%, respectively. The positive area of the first eigenvector is located in the Xiangjiang River basin south of 26°N with the value of 0.07. The negative area is located north of 26°N, and its center is located in the Wuling Mountain area in the northwestern Hunan and the Dongting Lake area in the northern Hunan with the value of −0.25 (Figure 3(c)). The negative area of the second eigenvector is mainly located north of the Xuefeng Mountain, but there is a positive area to the south of the Xuefeng Mountain, and the positive center is located in the southeastern Hunan with the value of 0.26 (Figure 3(d)).

Therefore, it can be concluded that the northwestern Hunan in the Wuling Mountains of the Dongting Lake basin and the southeastern Hunan on the northern foot of the Nanling Mountain are with the large-value variability of extreme precipitation, which are more prone to floods or droughts than other areas.

The time coefficients of the first two eigenvectors are analyzed statistically. The positive time coefficient represents the rainfall is more in the south and less in the north, and the negative one represents the opposite, so as to distinguish the positive and negative modes by the symbol of the time coefficient. The corresponding years of each mode are shown in Tables 2 and 3. For the annual maximum daily precipitation (Table 2), the first two eigenvector fields appear in 36 years of 1960–2016, accounting for 63.1%, which can basically present the characteristics of the main spatial distribution. For the annual maximum accumulated precipitation in a single rainfall event (Table 3), the first two eigenvector fields appear in 39 years, accounting for 68.4%, which can also present the characteristics of the main spatial distribution.

The numbers of years corresponding to positive and negative phases of each mode are roughly the same (Table 3 and Figure 4). The spatial distribution of extreme precipitation in the Dongting Lake basin exhibits a decadal oscillation of 10–20 years. The extreme precipitation in the 1960s was more in the north and less in the south, and then it turned to the opposite in the 1970s and 1980s, but it reversed to be more in the north and less in the south again in the 1990s.

The above analysis shows that the time coefficients of the first two eigenvectors of the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event have significant decadal characteristics. To analyze whether the decadal extreme precipitation has a spatial clustering, the global Moran's I and Z-score (Table 4) of the averaged annual maximum daily precipitation and the averaged annual maximum accumulated precipitation in a single rainfall event for each decade are calculated according to Equations (1) and (2). It can be seen that the extreme precipitation in the Dongting Lake basin has obvious spatial clustering characteristics, and the Z-score is greater than the critical value of 95% probability.

Based on the local indicators of spatial association, the spatial clustering of the decadal-averaged maximum daily precipitation and the decadal-averaged maximum accumulated precipitation in a single rainfall event in each decade is given in Figure 5. For the annual maximum daily precipitation, the ‘high–high’ clustering area is mainly located in the middle and lower reaches of the Yuanshui River in the northwestern Hunan and the southern part of the Lishui River basin. The ‘low–low’ clustering area is mainly located in the upper reaches of the Yuanshui River and the upper reaches of the Zishui River. For the annual maximum accumulated precipitation in a single rainfall event, the ‘high–high’ cluster area is mainly located in the upper reaches of the Xiangjiang River, followed by the middle and lower reaches of the Yuanshui River, and the ‘low–low’ cluster area is consistent with that of the annual maximum daily precipitation. The results in this study are consistent with the three spatial distribution patterns of northern, central and southern regions obtained by Long et al. (2020) using the SOM-k clustering method, indicating that it is advisable to use the Moran's I to analyze the spatial distribution of extreme precipitation.

The decadal variations show that the ‘high–high’ cluster area of annual maximum daily precipitation is relatively stable, mainly located in the northern and central basins. However, there is an obvious north–south oscillation in the ‘high–high’ cluster area of annual maximum accumulated precipitation in a single rainfall event, which is located in the northern part of the basin in the 1960s, in the southern part in the 1970s, in the central part in the 1980s, in the northern part in the 1990s and in the southern part from 2000 to 2016. This indicates that the maximum daily precipitation in each decade is relatively stable in the northern and central basins, but the clustering characteristics of the maximum accumulated precipitation in a single rainfall event are not obvious that may be affected by the different decadal drought–flood backgrounds.

The inter-annual variations of the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event are analyzed using the linear regression method. It can be seen from the linear trend distribution of annual maximum daily precipitation and annual maximum accumulated precipitation in a single rainfall event in the Dongting Lake basin (Figure 6) that the stations with the most significant increase of extreme precipitation are mainly located in the middle reaches of the Yuanshui River and the Zishui River, which are all along the Xuefeng Mountain. The stations with a decrease trend are mainly located in the southern basin. For the annual maximum daily precipitation, the most stations in the basin show an increasing trend (80 stations in Table 5), and only a few stations show a decreasing trend (17 stations). The annual maximum accumulated precipitation in a single rainfall event at 57 stations shows an increasing trend and that at 40 stations shows a decreasing trend.

The arithmetic average of the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event at all the stations in each sub-basin of Dongting Lake basin is calculated. The Mann–Kendall test is used to analyze whether there is an abrupt change in the inter-annual variations of the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event in each sub-basin. The Mann–Kendall test curves are shown in Figure 7. It can be found that there is an abrupt change period for the extreme precipitation in the basin, and it is from late 1980s to the early 1990s. After the 1990s, the extreme precipitation in each sub-basin shows an increasing trend, especially in the Zishui River basin.

To analyze the periodic variation of extreme precipitation in each sub-basin, the arithmetic mean of annual maximum daily precipitation and annual maximum accumulated precipitation in a single rainfall event at national meteorological stations in each sub-basin is calculated. The complex Morlet wavelet transform is used to calculate the real coefficients of wavelet transform and the wavelet variance of these two elements in each sub-basin (Figure 8). It can be seen from the real coefficients of wavelet transform of the annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event in each sub-basin (Figures 8(a) and 8(b)) that the extreme precipitation in each sub-basin has a certain quasi-period, but the differences in different regions are significant. The quasi-periodic characteristics in the Dongting Lake area and the Lishui River basin are the most significant, while that in the Yuanshui River basin is the least significant. It can be seen from the wavelet variance analysis (Figures 8(c) and 8(d)) that the quasi-period of extreme precipitation in the Dongting Lake area is about 20 years, and that in other sub-basins is about 10 years.

The analysis results from sections above preliminarily proved that the extreme precipitation in the Dongting Lake basin has the characteristics of inter-decadal variation, and more detailed demonstrations need to be further analyzed.

The spatial distribution of extreme precipitation is characterized in such a way that the large value is in the surrounding areas and the small value is in the central area of the Dongting Lake basin. The Lishui River basin, the lower reaches of the Yuanshui River and the middle reaches of the Zishui River are the areas with the maximum of extreme precipitation in the whole basin, and the Xiangzhong Basin is the area with the minimum. The topographic and terrain characteristics of the basin are the main factors that determine the spatial distribution of extreme precipitation. In the sub-basins, the averaged annual maximum daily precipitation from 1960 to 2016 is the largest in the Lishui River basin, and it is the smallest in the Zishui River basin; the averaged annual maximum accumulated precipitation in a single rainfall event is the largest still in the Lishui River basin, and it is the smallest in the Dongting Lake area.

The EOF decomposition of extreme precipitation in the Dongting Lake basin from 1960 to 2016 presents two typical modes of ‘north–south pattern’ and ‘northwest–southeast pattern’. The Lishui River basin in the Wuling Mountains and the Xiangjiang River basin on the northern foot of the Nanling Mountains are the areas with large extreme precipitation variability, being more prone to extreme precipitation events. The number of years corresponding to the positive and negative phases for the first and second modes of extreme precipitation in these 57 years is roughly the same, with 23 years corresponding to the first mode and 26 years corresponding to the second mode, which can well represent the main climatic characteristics of extreme precipitation in the basin.

The averaged extreme precipitation in each decade in the Dongting Lake basin has significant spatial clustering characteristics with the higher global Moran's I. There are two ‘high–high’ clustering areas. One is located in the northern basin and the other is located in the southern basin. The ‘low–low’ clustering area is from the upper reaches of the Zishui River to the upper reaches of the Yuanshui River.

The extreme precipitation in the Dongting Lake basin has an obvious north–south oscillation and the quasi-periodic variation. The numbers of years with the mode of ‘more in south and less in north’ and the mode of ‘less in south and more in north’ are roughly the same. The quasi-period of extreme precipitation in the Dongting Lake area is about 20 years, and that of other sub-basins is about 10 years. The annual maximum daily precipitation and the annual maximum accumulated precipitation in a single rainfall event at most meteorological stations in the whole basin show an increasing trend, and the area with the most significant increase is located in the middle reaches of the Yuanshui River and the Zishui River. The Mann–Kendall test shows that the late 1980s is the abrupt change period for the extreme precipitation in the basin. After the 1990s, the extreme precipitation in each sub-basin showed a significant increasing trend, especially in the Zishui River basin.

Generally, there are many factors that affect the spatial distribution of extreme precipitation. Based on the daily precipitation data at national meteorological stations, the obtained spatial distribution of extreme precipitation and the distribution of extreme precipitation in a return period can well present the spatial difference. To obtain more detailed spatial distribution characteristics, more surface regional meteorological observation data are needed. In addition, the spatio-temporal variation of extreme precipitation is closely related to the atmospheric circulation, and the establishment of quantitative forecast model of extreme precipitation based on various atmospheric circulation indexes is worth studying in the future.

This study is supported by the National Natural Science Foundation of China (42075077), the Operational Capacity Building Project of Hunan Meteorological Bureau (Phase III: NLJS01) and the National Key Research and Development Program of China (Grant No. 2018YFC1507604). We thank Dr Ruping Mo for helpful discussions. Constructive comments and suggestions from two anonymous reviewers greatly improved the manuscript.

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